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### Mathematics

 The category of mathematics are works on the abstract study of subjects encompassing quantity, structure, space, change, and more; it has no generally accepted definition.

### O Na Mole E Ke Anahonua (About the Roots of Geometry)

##### By: A. M. Legendre

1. O ke Anahonua ka mea e i ike ai ke ano o na mea i hoopalahaiahaia, oia na kaha, a me na ili, a me na paa. Ekolu mau ano o na mea i hoopalahaiahaia, he loa, he laula, a he manoanoa. 2. O ke kaha ; he loa wale no ko ke kaha; aole laula, aole manoanoa. O na welau o ke kaha he mau kiko ia: nolaila, o ke kiko, aole ona loa, aole laula, aole manoanoa, aka he wahi e ku wale ai no. 3. O ke kaha pololei ka loa pokole mai kekahi kiko a i kekahi kiko. 4. O ke kaha pololei o...

### Na Haawina Mua O Ka Hoailona Helu (First Lessons in Algebra)

##### By: Lahainaluna

Kuai kekahi keiki i ka ohia a me ka alani i na keneta he 12, no ia mau mea. Ua oi pakolu hoi na keneta o ka alani imua o ko ka ohia. Ehia na keneta o kela a o keia? E kau iho i ka w i hoailona no na keneta o ka ohia. A o ka w ke kumukuai i ka ohia, a he pakolu ko ka alani i ko ka ohia; nolaila, he mau w ekolu ke kumukuai i ka alani. He w hookahi ko ka ohia, a he akolu mau w ko ka alani, ina e huia lakou, he mau w eha o ka huina. Aka, he 12 na keneta i lilo no ia m...

Ua oi pa 4 aku na makahiki o Ioane imua o ko Iakobo; a o ka huina o ko laua mau. makahiki, he 20 ia. Ehia na makahiki o kela, o keia? E hoailona i na makahiki o Iakobo i ka w, no ka mea, he pa 4 na makahiki o Ioane i ko Iakobo, 4 mau w ka hoailona o kona mau makahiki. Nolaila, hookahi w a me 4 w, oia no 5 w ka huina o ko laua mau makahiki. Aka, he 20 ka huina o ko laua mau makahiki; nolaila, ua like 5 w me ka 20, a o ka w hookahi me ka hapa 5 o ka 20, oia na makahik...

### He Huinahelu (A Combined Arithmetic)

##### By: George Leonard

This volume contains basic mathematics (in Hawaiian). It teaches you the numbers in Hawaiian up to one hundred and also basio useful mathematics.

Ehia kahi iloko o ka 10? He 10 a me na kahi ehia iloko o ka 12? He 10 a me na kahi ehia iloko o ka 13? 14? 16? 19? 15? 18? 17? 11? Ehia na umi iloko o ka 20? iloko o ke 30? 40? 60? 80? 60? 70? 50? 90? 100? Ehia na umi a me na kahi iloko o ka 21? iloko o ka 23? 28? 26? 32? 35? 37? 44? 49? 41? 53? 57? 62? 65? 68? 71? 76? 99? 85? 87? 88? 92? 94? 99? He umi a me 1, heaha ia? 10 me 3? 10 me 7? 10 me 9? 2 umi? 2 umi me 1? 2 umi me 5? 2 umi me 7? 3 umi? 3 umi me 2? 3 umi me ...

### He Helu Kamalii (A Child's Arithmetic)

##### By: Wiliama Fowle

This volume teaches you children's basic arithmetic in Hawaiian.

No ka hana ana i keia Helu, e ahu no ke kumu i mau hua poepoe he kanaha a keu paha i mea heluia; pela no kela keiki keia keiki e ahu no lakou i na hua like. A like me ka hana ana a ke kumu, pela hoi e hana?i kela keiki keia keiki i kana mau hua iho.

### Principa Mathematica

##### By: Isaac Newton

Philosophiæ Naturalis Principia Mathematica, Latin for "Mathematical Principles of Natural Philosophy", often referred to as simply the Principia, is a work in three books by Sir Isaac Newton, first published 5 July 1687. Newton also published two further editions, in 1713 and 1726. The Principia states Newton's laws of motion, forming the foundation of classical mechanics, also Newton's law of universal gravitation, and a derivation of Kepler's laws of planetary motion ...

### Boole's Algebra of Logic 1847 : an Annotated Version of "Mathemati...

##### By: Stanley N Burris

This annotated version of Boole's "Mathematical Analysis of Logic" makes the extent to which Boole based his algebra of logic on the algebra of the integers. Problems are pointed out that will be dealt with in his famous 1854 "Laws of Thought"

The algebra Boole used in MAL to analyze logical reasoning is quite elementary, at least until the general theory starts on p. 60. But there is much that needs to be clarified---on many a page one can ask "Exactly what did Boole mean to say here?"

### On a New Method of Multiplication and Shortcuts : Volume 2

##### By: Artem Cheprasov

A completely new and unique method of multiplication where you can: 1.) Multiply positive numbers, get negative answers, and still achieve the correct positive result. 2.) Attach numbers to one another to bypass multiplication and addition steps. 3.) Choose one of many different paths to solve the same problem based on your own individual strengths and preferences. 4.) Multiply numbers into the billions with ease!

### Sketch of a Doctoral Program in Classical Mathematics : With an Em...

##### By: Jonathan Jacob Kenigson

This work is a brief set of notes; it has warrant neither to a claim of comprehensiveness nor of context. It represents the beginning of an odyssey toward realization of the classical ideal in mathematics education at the doctoral level.

### El número áureo en relatividad

##### By: Pedro Hugo García Peláez

El número áureo en relatividad Un libro científico sobre la razón de oro y una base de polinomios que satisfacen ese número

Pero al intentarlo con las transformaciones de lorentz que explican matemáticamente la teoría de la relatividad de Einstein, ya me convencí absolutamente que había demasiadas casualidades entre la teoría de la relatividad y el número áureo si considerábamos la fracción la velocidad de un objeto respecto a la velocidad de la luz igual a 0.681 o sea el inverso del número áureo. Metiendo estas relaciones en ambas fórmulas y aplicando logaritmos encontré hasta diez medic...

### Development strategies for the postal sector: an economic perspective

##### By: Dr. José Anson; Joëlle Toledano Bialot

This book examines the economics of the postal sector through three lenses: snapshot and trends, models, and opportunities. In the years to come, the Universal Postal Union plans to develop its role as a knowledge centre for the postal sector from these perspectives. At this time of radical transformation of the postal sector, it is important to understand how the sector has evolved historically, how it is connected with the economic system, and where it is heading. T...

### Onko Tonko : Puzzles for the Math Mentalist

##### By: Surajit Basu

This is a collection of puzzles requiring in most cases – high school math. The purpose is not necessarily to solve these problems, but to get you to think about different types of math puzzles. Many of the puzzles are introductions to different areas of math. Most of these puzzles can be done mentally. If you have to write, expect to write no more than a page. Pictures are useful.

“There are three planes”, said Onko, “which take off simultaneously - from Bangalore, Athens, and New York.” “Each plane goes 500 km north, then 500 km east, then 500 km south, and then 500 km west.” “Which plane is closest to its starting point?”, said Onko with a smile.

### Wandering in the World of Smarandache Numbers

##### By: A.A.K. Majumdar

In writing this book, the first problem I faced is to choose the contents of the book. Today the Smarandache Notions is so vast and diversified that it is indeed difficult to choose the materials. Then, I fixed on five topics, namely, Some Smarandache Sequences, Smarandache Determinant Sequences, the Smarandache Function and its generalizations, the Pseudo Smarandache Function and its generalizations, and Smarandache Number Related Triangles. Most of the results appea...

### Vedic Mathematics : 'Vedic' or 'Mathematics' : A Fuzzy & Neutrosop...

##### By: Florentin Smarandache; W. B. Vasantha Kandasamy

This book has five chapters. In Chapter I, we give a brief description of the sixteen sutras invented by the Swamiji. Chapter II gives the text of select articles about Vedic Mathematics that appeared in the media. Chapter III recalls some basic notions of some Fuzzy and Neutrosophic models used in this book. This chapter also introduces a fuzzy model to study the problem when we have to handle the opinion of multiexperts. Chapter IV analyses the problem using these mode...

We then remove the common factor if any from each and we find x + 1 staring us in the face i.e. x + 1 is the HCF. Two things are to be noted importantly. (1) We see that often the subsutras are not used under the main sutra for which it is the subsutra or the corollary. This is the main deviation from the usual mathematical principles of theorem (sutra) and corollaries (subsutra). (2) It cannot be easily compromised that a single sutra (a Sanskrit word) can be mathemat...

### Unfolding the Labyrinth : Open Problems in Physics, Mathematics, A...

##### By: Florentin Smarandache

Progress and development in our knowledge of the structure, form and function of the Universe, in the true sense of the word, its beauty and power, and its timeless presence and mystery, before which even the greatest intellect is awed and humbled, can spring forth only from an unshackled mind combined with a willingness to imagine beyond the boundaries imposed by that ossified authority by which science inevitably becomes, as history teaches us, barren and decrepit. ...

After the experiments were completed, the life span of such “atoms” was calculated theoretically in Chapiro’s works [61,62,63]. His main idea was that nuclear forces, acting between nucleon and anti-nucleon, can keep them far away from each other, hindering their annihilation. For instance, a proton and anti-proton are located at the opposite side of the same orbit and move around the orbit’s centre. If the diameter of their orbit is much larger than the diameter of the ...

### Scientia Magna : An International Journal : Volume 3, No. 3, 2007

##### By: Shaanxi Xi'an

Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics.

An identity involving the function ep(n) Abstract The main purpose of this paper is to study the relationship between the Riemann zeta-function and an in¯nite series involving the Smarandache function ep(n) by using the elementary method, and give an interesting identity. Keywords Riemann zeta-function, in¯nite series, identity. x1. Introduction and Results Let p be any fixed prime, n be any positive integer, ep(n) denotes the largest exponent of power p in n. Th...

### Scientia Magna : An International Journal : Volume 3, No. 4, 2007

##### By: Shaanxi Xi'an, Editor

Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics.

A structure theorem of right C-rpp semigroups1 Abstract A new method of construction for right C-rpp semigroups is given by using a right cross product of a right regular band and a strong semilattice of left cancellative monoids. Keywords Right C-rpp semigroups, right cross products, right regular bands, left cancellative monoids. x1. Introduction Recall that a semigroup S is called an rpp semigroup if all its principal right ideals aS1, regarded as right S1-sy...

### Scientia Magna : An International Journal : Volume 3, No. 2, 2007

##### By: Shaanxi Xi'an, Editor

Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics.

Abstract In this paper, we use 4-cyclotomic cosets of modulo n and generator polynomials to describe quaternary simple-root cyclic codes of length n = 85. We discuss the conditions under which a quaternary cyclic codes contain its dual, and obtain some quantum error-correcting codes of length n = 85, three of these codes are better than previous known codes. Keywords Quaternary cyclic code, self-orthogonal code, quantum error-correcting code. x1. Introduction Sinc...

### Scientia Magna : An International Journal : Volume 3, No. 1, 2007

##### By: Shaanxi Xi'an, Editor

This issue of the journal is devoted to the proceedings of the third International Conference on Number Theory and Smarandache Problems. The conference was a great success and will give a strong impact on the development of number theory in general and Smarandache problems in particular. In this volume we assemble not only those papers which were presented at the conference but also those papers which were submitted later and are concerned with the Smarandache type probl...

Abstract : Let k be any ¯xed positive integer, n be any positive integer, Sk(n) denotes the smallest positive integer m such that m! is divisible by kn: In this paper, we use the elementary methods to study the asymptotic properties of Sk(n), and give an interesting asymptotic formula for it. Keywords : F. Smarandache problem, primitive numbers, asymptotic formula.

### Scientia Magna : An International Journal : Volume 2, No. 4, 2006

##### By: Shaanxi Xi'an, Editor

Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics.

Smarandache inversion sequence Abstract We study the Smarandache inversion sequence which is a new concept, related sequences, conjectures, properties, and problems. This study was conducted by using (Maple 8){a computer Algebra System. Keywords Smarandache inversion, Smarandache reverse sequence. Introduction In [1], C.Ashbacher, studied the Smarandache reverse sequence: 1; 21; 321; 4321; 54321; 654321; 7654321; 87654321; 987654321; 10987654321; 1110987654321; (1...

### Scientia Magna : An International Journal : Volume 2, No. 3, 2006

##### By: Shaanxi Xi'an, Editor

Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics.

x3. Some Observations Some observations about the Pseudo-Smarandache Function are given below : Remark 3.1. Kashihara raised the following questions (see Problem 7 in [1]) : (1) Is there any integer n such that Z(n) > Z(n + 1) > Z(n + 2) > Z(n + 3)? (2) Is there any integer n such that Z(n) < Z(n + 1) < Z(n + 2) < Z(n + 3)? The following examples answer the questions in the affirmative:

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